OpenAI says AI system advances 10 major math problems

Summary

OpenAI says an internal version of its next major artificial intelligence model has produced new results on 10 longstanding problems in mathematics and theoretical computer science, highlighting the growing role of AI systems in advanced scientific research. The company said the results were generated by an internal version of Astra, described as its next major model. The issues had remained open with no progress on the main result for at least a decade in each case, and in many instances much longer.. The research spans areas including high-dimensional geometry, coding theory, group theory, operator algebras, quantum complexity, lattice cryptography and extremal combinatorics. OpenAI said the model produced results for issues of substantial interest to their respective mathematical communities, with several also having broader relevance across mathematics. Among the results, the system produced new upper bounds for high-dimensional sphere packing that reach down to the Cohn-Elkies threshold. It also generated improved bounds for the maximum size of binary codes at prescribed minimum distances, alongside related results for high-dimensional spherical codes. In group theory, OpenAI said the work included a construction establishing the existence of non-sofic groups, addressing a longstanding open question. The system also produced a disproof of Connes’s rigidity conjecture, which concerns whether certain groups are uniquely determined by their von Neumann algebras. Other results involved arithmetic circuit complexity, including new lower bounds for computing the permanent using arithmetic circuits and formulas. OpenAI said the work included an arithmetic-formula lower bound of order n⁴/log n. READ: AI just got cheaper: OpenAI slashes prices by up to 80% (July 31, 2026) The model also produced an exponential parallel repetition theorem for general two-player quantum games, extending a foundational principle from classical complexity theory. In lattice-based mathematics, the research produced a polynomial-factor hardness of approximation result for the closest vector problem, a foundational question with connections to post-quantum cryptography. The remaining results covered Ehrhart’s volume conjecture, multicolor Ramsey numbers and extremal graph theory. OpenAI said the work on multicolor Ramsey numbers produced a superexponential lower bound for multicolor t…